The Effects of Multi-Task Learning on ReLU Neural Network Functions

• URL: http://arxiv.org/abs/2410.21696v2
• Date: Tue, 05 Nov 2024 22:03:21 GMT
• Title: The Effects of Multi-Task Learning on ReLU Neural Network Functions
• Authors: Julia Nakhleh, Joseph Shenouda, Robert D. Nowak,
• Abstract summary: We show that neural network learning problems with large numbers of diverse tasks are approximately equivalent to an $ell2$ (Hilbert space) problem over a fixed kernel determined by the optimal neurons.
• Score: 17.786058035763254
• License:
• Abstract: This paper studies the properties of solutions to multi-task shallow ReLU neural network learning problems, wherein the network is trained to fit a dataset with minimal sum of squared weights. Remarkably, the solutions learned for each individual task resemble those obtained by solving a kernel method, revealing a novel connection between neural networks and kernel methods. It is known that single-task neural network training problems are equivalent to minimum norm interpolation problem in a non-Hilbertian Banach space, and that the solutions of such problems are generally non-unique. In contrast, we prove that the solutions to univariate-input, multi-task neural network interpolation problems are almost always unique, and coincide with the solution to a minimum-norm interpolation problem in a Sobolev (Reproducing Kernel) Hilbert Space. We also demonstrate a similar phenomenon in the multivariate-input case; specifically, we show that neural network learning problems with large numbers of diverse tasks are approximately equivalent to an $\ell^2$ (Hilbert space) minimization problem over a fixed kernel determined by the optimal neurons.

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